Question

The volume of a rectangular box is 270 m3. The width of the box is 3 meters less than the length. The height is 5 meters. What is the length of the box?

Answer 1

V=LWH, W=L-3, H=5, V=270

L(L-3)5=270

5L^2-15L=270

5L^2-15L-270=0

L^2-3L-54=0

L^2+6L-9L-54=0

L(L+6)-9(L-6)=0

(L-9)(L+6)=0

Since L>0

L=9 meters

Answer 2

The length of the box is 9 meters

Explanation:

The formula of a Right Rectangular Prism is

V=L*W*H

Where,

L= the length

W=the width

H= the height

In this case,

V =270 m³

height=5 m

width = length-3m

Isolating the Length

V=L*W*H

L=V/W*H

L=V/(L-3)*H

L*(L-3)=V/H

L²-3L= 270/5

L²-3L= 54

L²-3L-54= 0

We can use Quadratic Formula.

If we have an equation with the following Standard Form , ax² + bx + c = 0

we can solve the equation applying the Quadratic Formula.

x = (−b ± √(b^2 − 4ac))/ 2a

In this case

a=1

b=-3

c=-54

x = (3 ± √(-3^2 − 4*1*-54))/ 2*1

x = (3 ± √(9 + 216))/ 2

x = (3 ± √(225))/ 2

x = (3 ± 15)/ 2

x = (3 - 15)/ 2 x = -12/2=-6 can´t be negative

x = (3 + 15)/ 2 x = 18/2=9